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A preconditioning proposal for ill‐conditioned Hermitian two‐level Toeplitz systems
Author(s) -
Noutsos D.,
Capizzano S. Serra,
Vassalos P.
Publication year - 2004
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.398
Subject(s) - toeplitz matrix , hermitian matrix , computation , mathematics , mathematical optimization , function (biology) , computer science , algebra over a field , algorithm , pure mathematics , evolutionary biology , biology
Abstract Large 2‐level Toeplitz systems arise in many applications and thus an efficient strategy for their solution is often needed. The already known methods require the explicit knowledge of the generating function ƒ of the considered system T nm (ƒ)x= b , an assumption that usually is not fulfilled in real applications. In this paper, we extend to the 2‐level case a technique proposed in the literature in such a way that, from the knowledge of the coefficients of T nm (ƒ), we determine optimal preconditioning strategies for the solution of our systems. More precisely, we propose and analyse an algorithm for the economical computation of minimal features of ƒ that allow us to select optimal preconditioners. Finally, we perform various numerical experiments which fully confirm the effectiveness of the proposed idea. Copyright © 2004 John Wiley & Sons, Ltd.